Bonus: simplify with gems

Hello, and welcome to Myriora Maths! Here's a fraction: eighty-four over one hundred and twenty-six. It looks complicated. But it's the same amount as a much simpler fraction. Gems can show us which one.

First, why can a fraction get simpler? Two over four, and one over two, shade the same amount of the bar. The numbers change, but the amount doesn't.

Let's start small, with six over fifteen. Six is a two and a three. Fifteen is a three and a five. There's a three on the top, and a three on the bottom. Take them both out. That's the same as dividing the top and the bottom by three. So the amount stays the same. Two over five is left.

Now for our big fraction. Eighty-four is two, two, three and seven. One hundred and twenty-six is two, three, three and seven. They share a two. They share a three. And they share a seven. Take out all of those pairs. A two is left on top, and a three on the bottom. So it's two over three.

How do you know you've finished? The top and the bottom have no more gems to share. Then the fraction is in its simplest form.

Let's try one together. Simplify twelve over thirty. Here's a tip: split the top and the bottom into gems. Say it out loud!

Twelve and thirty share a two and a three. Take them out, and two over five is left.

Here's a common mistake. Let's simplify six over eighteen. Take out the pairs, and the top has no gems left. So you might write a zero. But taking gems out means dividing, and six divided by six is one. So the answer is one over three.

Your turn! What is the simplest form of eighteen over twenty-four? Pick the right card. You've got ten seconds, or pause the video. Go!

Time's up! The answer is three over four! They share a two and a three. Six over eight and nine over twelve are the same amount, but they aren't finished.

Quick review. Split the top and the bottom into pure gems. Take out each pair they share. If a whole side goes, a one is left. No more pairs means simplest form. See you next time!